Variable resistor

ABSTRACT

A resistive element has a gradient of resistivity extending along its length. It is held in slidable contact with two or more brushes spaced-apart from each other. The resistance between the brushes can be varied by changing their position relative to the resistive element and the gradient or resistivity. The resistive element may have an arcuate configuration and the relative position may be changed by rotating the element. Two such variable resistors having a logarithmic resistance gradient may be combined in a variable resistance attenuator.

United States Patent Kogo et a1.

1 1 VARIABLE RESISTOR [75] Inventors: Masanori Kogo; Hisashi Honda,

both of Tokyo, Japan [73] Assignee: Nippon Electric Company, Limited,

Tokyo, Japan Notice: The portion of the term of this patent subsequentto Sept. 18, 1990, has been disclaimed.

[22] Filed: June 20, 1973 [21] Appl. No.: 371,620

Related US. Application Data [63] Continuation-impart of Ser. No.267,630, June 29,

1972, Pat. NO. 3,760,322.

[30] Foreign Application Priority Data June 30, 1971 Japan 46-48316 [52]US. Cl. 338/89; 338/137; 338/142; 338/150; 333/81 R [51] Int. Cl. 1101C10/04; HOIC 10/26 [58] Field of Search 338/89, 137, 138-142, 338/150;333/81 R [56] References Cited UNITED STATES PATENTS 1,731,772 [0/1929Greenewalt 338/141 X 1*June 17, 1975 2,005,922 6/1935 Stoekle 338/1402,096,027 10/1937 Bode H 333/81 X 2,681,967 6/1954 Harrison et a1...338/89 2,798,140 7/1957 Kohring 338/137 2,854,643 9/1958 Wigan et a1333/81 2,881,295 4/1959 Brown 338/137 X 3,657,688 4/1972 Casey et a1.338/150 Primary Examiner-J. V. Truhe Assistant Examiner-D. A. ToneAttorney, Agent, or FirmHopgood, Calimafde, Kalil, Blaustein & Lieberman1 7 1 ABSTRACT A resistive element has a gradient of resistivityextending a1ong its length. It is held in slidable contact with two ormore brushes spaced-apart from each other The resistance between thebrushes can be varied by changing their position relative to theresistive element and the gradient or resistivity. The resistive elementmay have an arcuate configuration and the relative position may bechanged by rotating the element. Two such variab1e resistors having alogarithmic resistance gradient may be combined in a variable resistance attenuator.

3 Claims, 13 Drawing Figures PATENTEDJUN 17 ms SHEET [IMAM/451D;

(PR/0R ART) FIG. la WWW? 5 FIG. 26

(PRIOR ART) Fl GI b PMENTEDJUN 17 1975 3' 8 SHEET 3 '43 (=IZII/IZII)VARIATION 0P4; f y/ w/ru RESPECT r0 THE LENGTH ,r(4r 100 MH FIG. 8

DJ Du TD fi CV Cu PATENTEDJUN 17 I975 SHEET 2a ea 90 100616) MOVEMENTRATE OF BPUSHFS 0F VAfi/AHLE kfslsraks FIG. II

1 VARIABLE RESISTOR RELATED APPLICATIONS This is a continuation-in-partof an application entitled Variable Resistor Ser. No. 267.630 filed June29, I972 now US. Pat, No. 3,760,322 and the benefit of the filing dateof that application is claimed.

BACKGROUND OF THE INVENTION This invention relates to a variableresistor for use in electrical circuits and, more specifically, to avariable resistor including a film of resistive material having agradient of resistivity in a predetermined direction.

In a conventional variable resistor, terminals are provided at the endsof the resistive film and a brush is held in slidable contact with thefilm to provide a variable resistance between one of the terminals andthe brush. The resistance then depends on the position of the brush withrespect to the film.

One of the shortcomings of this type of variable resistor is that theinductance component appearing in parallel with the variable resistanceundergoes a considerable change depending on the resistance selected. Aprincipal object of the present invention is therefore to provide avariable resistor capable of resistance variation without causing achange in the inductance component.

SUMMARY OF THE INVENTION The variable resistor of the present inventioncomprises a resistive element having a gradient of resistivity thatvarys in a predetermined manner along its length and at least twobrushes separated by a predetermined interval and held in slidablecontact between the resistive element. The desired gradient ofresistivity can be given to the resistive element by tapering its widthor gradually changing its composition. More than two slidable brushesmay be used as required When more than two brushes are used, a differentvariable resistance can be obtained across every two brushes. Thebrushes are interconnected so that the distance between them remainsconstant.

In the variable resistor of this invention, a desired variableresistance is provided between the slidable brushes, while maintainingthe accompanying inductance component at a fixed value.

Another feature of the present invention is that the variable resistancenever takes the value zero ohms. This contributes to the simplificationof a circuit including a finite minimum resistance.

BRIEF DESCRIPTION OF THE DRAWINGS The present invention will now bedescribed with reference to the accompanying drawings, in which:

FIGS. la and b show equivalent circuits of a conventional variableresistor for the direct-current and extremely low frequency region andfor the high frequency region, respectively;

FIGS. 2a and b show equivalent circuits of an embodiment of theinvention for the direct-current and low frequency region and for thehigh frequency re' gion, respectivelyf FIG. 3 is a cross-sectional viewof a first embodiment of the invention;

FIG. 4 shows a circuit diagram of a bridged-T type variable resistanceattenuator to which this invention is applicable;

FIG. 5 shows a cross-sectional view of a second embodiment of thisinvention adapted to the attenuator of FIG. 4;

FIG. 6 is an equivalent circuit of a third embodiment of the invention;

FIG. 7 is an equivalent circuit of a fourth embodiment of the invention;

FIG. 8 shows diagramatically, the impedance variation characteristics ofthe invention as compared to those of a conventional variable resistor;

FIG. 9 shows diagramatically, the frequency charac teristics of theconventional bridged-T type variable attenuator and those of theattenuator of FIG. 4 in comparison with the second embodiment of theinvention shown in FIG. 5;

FIG. 10 shows diagramatically, the attenuation values of a conventionalattenuator and the attenuator of FIG. 4 and the resistance values ofvariable resistors Rs and Rp used therein, as a function of the movementof brushes of the variable resistors; and

FIG. 11 shows diagramatically, the resistance variation of the variableresistors Rs and Rp which are used in the variable resistance attenuatorof FIG. 4, with respect to the movement of the brushes of the variableresistors.

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. la shows an equivalentcircuit for conventional variable resistor comprising a resistive film10 having terminals 1 and 3 at its ends, and a slidable brush 2opcrating in the low frequency range. The desired variable resistance isobtained between the brush 2 and the terminal 3. The resistive film 10has a uniform specific resistance, and its inductance component isproportional to the length, but negligibly small when a direct currentor extremely low frequency signal is applied. Likewise, the capacitivecomponent is also negligible. Generally, the impedance Z between theterminals 1 and the brush 2 is given by:

Z =x R'+w"-L (2 where R stands for the resistance per unit length of theresistive film 10; L, for the inductance per unit length of the film 10;x, for the length of the section of the film 10 lying between theterminal I and the brush 2; and w, for the angular frequency.Differentiating Eq. (2) with respect to x and w,

dIZ I/dx= W I III =WL XI JRE'I'WELI 4 From Eqs. (3) and (4), it isapparent that I Z, I increases linearly with each successive incrementof the length x, and non-linearly with each successive increment of theangularfrequency w.

The impedance Z of an ideal variable resistor having neither acapacitance component nor an inductance component may be expressed asfollows:

0 I oI (5) where resistive film is assumed to have a uniform specificresistance R. The ratio A of I 2 I to I Z is given by:

-Continued More specifically. the absolute value of impedance is alwayslarger in the conventional variable resistor than in the ideal variableresistor. Also. the larger the angular frequency w. or the smaller thespecific resistance R of the resistive film. the greater the ratio A ofEq. (6) becomes.

In other words. with the increase of the frequency. the impedance has agreater effect on the variable resistance. making the deviation from theideal variable resistor g eater. An equivalent circuit for aconventional variabl resistor at high frequency is shown in FIG. lb.

In the equivalent circuits of the variable resistor of the inventionshown in FIGS. and 2b, slidable brushes 5 and 6 are in contact with aresistive film 30. The film (resisti've element) has a nonlineargradient of resistivity with respect to its length. Two brushes 5 and 6,spaced apart by a predetermined interval. are held in slidable contactwith the resistive film 30. The interval between the brushes and thenonlinear gradient in the resistivity of the film 30 are selected sothat the resistance between the brushes 5 and 6 exhibits an increase inlinear proportion to the lengthwise movement of the brushes. It will beappartent, however. that the invention is not limited to this resistivefilm arrangement. In general. the gradient may change continuously.linearly or nonlinearly. For simplicity in this explanation. it isassumed here that the incremental change in the gradient. in otherwords. the rate of the change of the resistivity of the film 30. is inlinear proportion to the position selected along its length.

Assuming that the distance from the lefthand end of the resistive film30 to the brush 6 is x, the resistance therebetween is .rR. and thespatial interval between the brushes 5 and 6 is unity. then theimpedance Z between the brushes 5 and 6 can be expressed as:

|Z,|= .r R+ x where .r g l and the variables are the same as those inEqs. (I) and (2). The ratio AQof the impedance 1 Z of the presentvariable resistor to the impedance I Z.,\ of the ideal variable resistoris given by:

where x g I.

As in the case of Eq. (6), Eq. (9) indicates that the impedance of thepresent variable resistor is always larger than that of the idealvariable resistor. and that the value of A, is increased with theincrease in the angular frequency w. Also. as the resistance .rR isincreased, the present variable resistor approaches the ideal variableresistor in its characteristics.

Derived from Eqs. (2) and (3), the ratio A of the absolute value of theimpedance of the present variable resistor to that of the conventionalone is given by:

It follows that A l.O where .l 2 l.

In other words. in the range ofx ll). the variable impedance Z of thepresent variable resistor is smaller than that Z, of the conventionalresistor and closer to that of the ideal resistor. FIG. 8 shows thevalue of A; given in Eq. (IO) with respect to the length x.

In such a variable resistor. the resistance obtained across the brushes5 and 6 cannot take the value zero ohms even under the state of unitythus maintaining a certain minimum resistance value. The variableresistor of this invention is therefore highly desirable for thosecircuits which require a minimum constant resistance.

Referring now to FIG. 3, the first embodiment of the invention, anequivalent circuit of which is shown in FIG. 2, two brushes 106 and 107are attached to a cylindrical housing 105 and held in contact with anarcuate resistive film 102 attached to a disc-shaped base 103. The film102 may form a complete circle. The resistive film 102 has a nonlineargradient of resistivity in the circumferential direction. This gradientis attained by tapering the thickness or the width of the film I02.Alternatively, it may be attained by varying the composition of thematerial of which the film is made. By the expression gradient ofresistivity it is meant that the resistance per unit length of the filmvaries in a predetermined manner as it is measured at different pointsalong its length. The base 103 is pressed downwardly by a spring 104thus permitting rotation under the control of a rotatable disc 101. Thedesired variable resistance value is thus obtained between the brushes106 and 107. by changing the relative position of the brushes and thefilm 102.

Referring now to FIG. 4, a bridge-T type variable attenuator using thevariable resistors of the present invention permits a variation in theattenuation depending on the selected resistance of two resistors Rs andRp. A variable resistor Rs is connected across the input terminal 41 andthe output terminal 43, and two fixed resistors R0 and R0 are connectedin parallel with the variable resistor R A variable resistor Rp isconnected across the connection point 44 of the two fixed resistors R0and R0 and the input-output common terminal 42. In each of the variableresistors Rs and Rp. the interval between the brushes 45 and 46 (47 and48) and the nonlinear gradient in the resistivity of the film 49 (50)are selected so that the resistance between the brushes 45 and 46 (47and 48) exhibits an increase in logarithmic proportion to the lengthwisemovement of the brushes 45 and 46 (47 and 48). Moreover, the variableresistors Rs and Rp are interlocked to operate so that when oneresistance is increasing, the other is decreased. When conventionalvariable resistors are used in this attenuator, the voltage standingwave ratio (VSWR) is unavoidably increased with an increase in thefrequency. This tends to cause an increase in the impedance 2..

Referring now to FIG. 5, a second embodiment is shown which is adaptedto the variable attenuator of (ill FIG. 4 and has a dual variableresistor which may be viewed as two separate variable resistors. Each ofthese variable resistors is the equivalent to one resistor of thecircuit shown in FIG. 2. The dual variable resistor has two brushes H6and II7 fixed to a base 119 which also serves as a cover. Two arcuateresistive films I12 and "2' having nonlinear resistivity gradients areattached to bases I13 and 114 and kept in slidable contact with thebrushes I16 and 117. The resistive films H2 and I12 are moved as a disc101 on which the bases I13 and 114 are mounted is rotated. Theseelements are contained in a cylindrical housing 105 and a closureincluding a base 119. A pair of brushes are provided for each of theresistive films 112 and H2.

With the dual variable resistor of FIG. 5 used as the resistors Rs andRp of the bridged-T type variable attenuator of FIG. 4, the impedancesof the resistors Rs and Rp exhibit virtually no change in the inductivecomponents, as indicated by Eq. (7). Therefore, the voltage standingwave ratio (VSWR) can be kept unchanged as shown in FIG. 9, whichillustrates two groups of curves showing the attenuation vs. frequencyand the voltage standing wave ratio (VSWR) vs. fre quencycharacteristics of the present variable attenuator as compared withthose of a conventional variableresistor-based attenuator.

In the bridged T type variable attenuator of FIG. 4, the resistances r,and r, of the resistors Rs and Rp can be expressed as a function of theattenuation value e as follows:

r e (e" I) r, e (e" l) where a is given in neper.

The zero attenuation value is achieved by making the resistance r, andr, zero and infinity, respectively. Con versely, infinite attenuation isachieved by making r, and r, inifinity and zero, respectively.Practically, however, these requirements cannot be met, because infiniteimpedance is difficult to achieve with a conventional variable resistor.This results in a residual attenuation which causes a high voltagestanding wave ratio. Therefore, to achieve a satisfactorily low voltagestanding wave ratio with the conventional device, at least one resistormust be in series with either Rs or Rp or both. In contrast, thevariable resistor of the invention never takes the value zero ohms. Thismakes it possible to dispense with any additional resistance elementsand consequently to simplify and miniatuarize the attenuator as a whole.This applies to any apparatus or device in which the present inventionfinds application.

Now, other advantages of the variable attenuator of FIG. 4 will beexplained.

It is required for the purpose of inserting a bridged-T type variableresistance attenuator into a transmission line without changing thecharacteristics of the transmission line that resistors of theattenuator satisfy the following equation "l "n "o (I3) where r, standsfor a resistance value of each fixed resistor R0. In general, anattenuation value of the bridge- T type attenuator is adjusted bychanging the resistances r, and r, of the variable resistors Rs and Rp.Therefore, the above equation I3) should be satisfied regardless of theadjusted attenuation value, for the mention purpose. In order to meetequation (13), the conventional bridgedT type attenuator employs avariable resistor Rs of such a type that the resistance increases inlinear proportion to the movement of the brushes and a variable resistorRp of such a type that the resistance increases in inverse proportion.In such conventional attenuators. it is difficult to provide a variableresistor Rp having the desired inverse resistance variation, becausestrict controls are needed for the area resistance and width of theresistance film thereof. Therefore. the yield and manufacturingefficiency are small. and the manufacturing cost is usually about two orthree times higher than that of the variable resistor Rs having a linearresistance variation. Also, since variable resistors Rs and Rp havedifferent resistance variations, it is not possible to interchange thevariable resistor Rs with Rp or vice versa, where attenuation value orcharacteristic impedance is changed.

In contrast, both the variable resistors Rs and Rp of the attenuator ofFIG. 4 have a structure such that resistanee increases or decreases inlogarithmic proportion to the movement of brushes. Therefore, thevariable resistors Rs and Rp can be interchanged, and, moreover, theattenuator of FIG. 4 always satisfies equation (13).

FIG. 10 shows the attenuation values (ATT) of a conventional attenuatorand the attenuator of FIG. 4 and the resistance values of variableresistors Rs and Rp used in the conventional attenuator and in theattenuator of FIG. 4, all as a function of the movement of the brushesof the variable resistors Rs and Rp. As will be understood from FIG.II], the variable resistor Rp having the logarithmic variation of theresistance value r,, (dotted line) has a smaller variation gradient ofthe resistance than that of the resistor having the reciprocal variationof the resistance value r, (solid line). This reveals the ease ofmanufacture of the resistor Rp of the invention.

In designing electronic equipment such as transmission equipment, it ispreferable, to avoid the use of variable resistance attenuators. If theuse of such attenuators is not avoidable, they should be used in aregion where the attenuation value thereof is small. In this respect, aswill be apparent from comparison of the ATT curves of FIG. 10, thevariable resistance attenuator of this invention is more suited forselecting a small attenuation value than the conventional attenuator.Hence the attenuator or this invention is suitable for use intransmission equipment.

FIG. II shows the resistance variation of the resistors Rs and Rp of theattenuator of this invention; the move ment of the brushes of thevariable resistors is presented along the abscissa and the resistancevalue is represented along the ordinate on a logarithmic scale to showthe resistance values r,, and r, of the variable resistors Rp and Rs.Both the resistances r, and r are selected to vary logarithmically withrespect to the movement of the brushes, but their variations are inopposite directions. Hence, in FIG. 11, resistances r and r, are shownas straight lines declining in opposite directions.

In FIG. 11, three pairs of resistances r and r,,, r,, and r,,, and r,,;and r are shown. However, for resistances r and r, belonging to eitherthe same pair or different pairs the value of r,,,- X r (both i and jstand for 1,2 or 3) is always equal to the second power of theresistanee value at an intersection of the straight lines r,,,- and r,;.In effect, for a variable resistance attenuator having a characteristicimpedance of ohms (corresponding to r,, of equation 13 variableresistors Rs and Rp having resistance values r and respectively. may beselected. In the same way. for the characteristic impedance of 50 ohms,variable resistors Rs and Rp having resistance values r and r 2.respectively. may be selected. and for the characteristic impedance of300 ohms, variable resistors Rs and Rp having respectively resistances rand r... may be selected.

An additional advantage of the resistance attenuator of FIG. 4 is thatone variable resistor may be used as either Rs or Rp. It can be pointedout as another advantage that one variable resistor can be used in avariable resistance attenuator having any characteristic impedance.These advantages are attributed to the fact that the variable resistorshaving a logarithmic resistance variation are used as both variableresistors Rs and Rp of the variable resistance attenuator. This allowsmass production of variable resistance attenuators having one or morecharacteristics with fewer kinds of variable resistors and contributesto reduced losses.

Referring now to FIG. 6, a third embodiment of this invention has fourbrushes 202, 203, 204, and S spaced at predetermined intervals and heldin slidable contact with a resistive film 201. This variable resistormakes it possible to obtain two desired variable resistance values fromone resistive film 201, one from the brushes 202 and 203 and the otherfrom the brushes 204 and 205. In other words. a dual variable resistorcan be constructed using one resistive film 201. Brushes 203 and 204 maybe connected to each other when these two brushes are to be at an equalpotential. It will be apparent that more than four brushes can be used.

Referring now to FIG. 7, the fourth embodiment of the invention includesa resistive film 301 having terminals 304 and 305 at its ends,respectively, and brushes 302 and 303 held in slidable contact with theresistive film 301 with a voltage is applied between the terminals 304and 305, the desired voltage is derived from the brushes 301 and 303. Inthis variable resistor, the inductive component of the output impedanceis small and constant. Therefore, the use of this variable resistor in ahigh frequency device will contribute substantially to betterperformance.

In the foregoing description. we have explained the present inventionwith reference to several exemplary embodiments and their application.However it will be apparent to those skilled in the art that othermodifications are possible without departing from the spirit and scopeof the invention.

We claim:

I. A variable resistance attenuator comprising an input terminal. anoutput terminal. a common terminal. a first variable resistor connectedbetween said input terminal and said output terminal. first and secondresistors connected in series between said input terminal and saidoutput terminal. and a second variable resistor connected to the seriesconnection between said first and second resistors and connected at itsopposite terminal to said common terminal, said first and secondvariable resistors each comprising an electrically resistive element.the incremental resistance of which varies along its length, to form agradient of resistivity. and two brushes spaced apart by a constantdistance in slidable contact with each said resistive element. said gradient being such that the resistance between the brushes varieslogarithmically. but the inductance between them remains substantiallyconstant as they are moved with respect to the gradient.

2. A variable resistor comprising an electrically resis tive element theincremental resistance of which varies along its length to form agradient of resistivity. and two moveable brushes spaced apart by afixed distance and in slidable contact with the resistive element, theresistive element providing a substantially constant inductance and alinearly variable resistance as the position of the brushes with respectto the gradient is varied.

3. A variable resistor comprising an electrically resistive element theincremental resistance of which varies along its length to form agradient of resistivity, and two moveable brushes spaced apart by afixed distance and in slidable contact with the resistive element, theresistive element providing a substantially constant inductance and alogarithmically variable resistance as the position of the brushes withrespect to the gradient is varied.

1. A variable resistance attenuator comprising an input terminal, anoutput terminal, a common terminal, a first variable resistor connectedbetween said input terminal and said output terminal, first and secondresistors connected in series between said input terminal and saidoutput terminal, and a second variable resistor connected to the seriesconnection between said first and second resistors and connected at itsopposite terminal to said common terminal, said first and secondvariable resistors each comprising an electrically resistive element,the incremental resistance of which varies along its length, to form agradient of resistivity, and two brushes spaced apart by a constantdistance in slidable contact with each said resistive element, saidgradient being such that the resistance between the brushes varieslogarithmically, but the inductance between them remains substantiallyconstant as they are moved with respect to the gradient.
 2. A variableresistor comprising an electrically resistive element the incrementalresistance of which varies along its length to form a gradient ofresistivity, and two moveable brushes spaced apart by a fixed distanceand in slidable contact with the resistive element, the resistiveelement providing a substantially constant inductance and a linearlyvariable resistance as the position of the brushes with respect to thegradient is varied.
 3. A variable resistor comprising an electricallyresistive element the incremental resistance of which varies along itslength to form a gradient of resistivity, and two moveable brushesspaced apart by a fixed distance and in slidable contact with theresistive element, the resistive element providing a substantiallyconstant inductance and a logarithmically variable resistance as theposition of the brushes with respect to the gradient is varied.